The third generation of the 300-letter series Chrysler(s)

The 1960 model offered a 375 hp (280 kW) "Cross-Ram" version of the 413 cu in (6.8 L) Wedge Head V8 introduced in 1959. To boost power at lower and mid RPMs, a special intake manifold was derived. Instead of the normal V8 central intake manifold with the carburetor(s) on top, the cross-ram consisted of two pairs of 30 in (760 mm) long-tuned pipes that crisscrossed so that each set fed the opposite side of the engine. The carburetors and air cleaners hung off the sides of the engine over the fender wells. These long tubes were tuned so that resonances in the column of air helped force air into the cylinders at those engine speeds.

A special 400 hp (300 kW) "short ram" version optimized for higher engine speeds was produced for competition. The overall tube length remained at 30", but the tuned portion of the stacks was only 15 in (380 mm), favoring high RPMs. Only 15 "short ram" cars were produced; these were also fitted with the exotic but often troublesome French manufactured Pont-a-Mousson 4-speed manual transmissions developed for the Chrysler-powered Facel Vega. Approximately 4 of these "Special Gran Turismo" are known to exist, including one convertible and one with air conditioning; it is believed that 15 were originally produced.

Also new were four individual, leather bucket seats for front and rear passengers with a full-length console from the dash to rear seatback which had previously been introduced on the Chrysler Norseman concept car of 1956. The rear passenger electric window switches were installed in the center console within easy reach, and bench seats for front and rear passengers were no longer available. The rear bucket seats were also offered on the New Yorker Custom coupe. Swiveling front seats were fitted as standard equipment but were modified to mechanical operation only initiated by the driver and not synchronized to the door when opened. The AstraDome instrument cluster was introduced on all Chrysler products only and featured "Panelescent Lighting" and a tachometer was installed in the center console below the radio due to the complexity of the three-dimensional instrument cluster. The exterior color list was shortened to Formal Black, Toreador Red metallic, Alaskan White, and Terra Cotta metallic while the standard interior color remained as tan leather.

The dash had been designed with Chrysler's push-button controls for the TorqueFlite automatic in mind, with the "AstraDome" instrument cluster covering the part of the steering column a column shifter would come out from under then-standard practice, so manual cars used a floor shifter. Due to the installation of the "AstraDome" instrument cluster extending outward towards the steering wheel, the traditional installation of the turn signal lever was relocated to the dashboard underneath the "TorqueFlite" pushbutton gear selectors and was installed as a sliding lever that would return to center as the steering wheel returned to the center position. To the right of the steering wheel but left of the radio were pushbutton controls for the ventilation and air conditioning while retaining the use of a lever for temperature control.

The bodywork was also redone for 1960, using Chrysler's new lightweight unibody construction and given sharper-edged styling with outward-tilting fins that were visually separated from sides, while the front grille adopted the corporate look used by all Chrysler-branded products, ending a tradition where the 300 had unique styling not shared with other Chrysler branded vehicles. A controversial "Continental"-style trunk lid appeared, shared with the Imperial and was gone for 1961.

Sales increased to 969 coupes and 248 convertibles with a suggested retail price of US$5,411 ($49,563 in 2021 dollars) for the hardtop coupe and US$5,841 ($53,502 in 2021 dollars) for the convertible.